Abstract
In this paper we establish two theta function identities with four parameters by the theory of theta functions. Using these identities we introduce common generalizations of Hirschhorn-Garvan-Borwein cubic theta functions, and also re-derive the quintuple product identity, one of Ramanujan’s identities, Winquist’s identity and many other interesting identities.
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Supported by Innovation Program of Shanghai Municipal Education Commission and PCSIRT
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Yang, X.M. The products of three theta functions and the general cubic theta functions. Acta. Math. Sin.-English Ser. 26, 1115–1124 (2010). https://doi.org/10.1007/s10114-010-8435-6
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DOI: https://doi.org/10.1007/s10114-010-8435-6